core

### Primary Datum Plane Math Types

The Math Types area of the constructed Primary Datum Plane provides three different math types. These math types support the ASME and ISO datum plane standards.

The three math types in the first drop-down list of the Math Types are:

- CONSTRAINED_L1

- CONSTRAINED_L2

- CONSTRAINED_MINMAX

#### Definitions

These terms correspond to the following definitions in the standards:

PC-DMIS | ASME Y14.5 | ISO 5459
Constrained L1 | Alternative Math Type | Alternative Math Type
Constrained L2 (default) | Alternative Math Type | Alternative Math Type
Constrained minmax | Alternative Math Type | Default Math Type

Before you choose a math type, you need to understand the concepts of void filtering (external envelope), norms, and outside-material constraint (constrained fit). These are covered below:

Void Filtering

Void filtering is also known as the external envelope.

In reality, surfaces of planar features are not planar. Surfaces have both convex and concave regions (peaks and valleys). The concave regions are guaranteed to never contact a perfectly flat surface plate. These are known as "voids". The software can filter out these voids by interpolating over them. Since the voids do not affect how the part interacts with an ideal surface plate, you may want to filter out the voids:

Illustration of a void-filtered surface. The dotted gray line is the real surface feature. The solid black line is the void filtered surface. The space between the real feature surface and the void filtered surface are the voids.

Norms

In general, ideal geometric shapes are fitted to non-ideal surfaces by minimizing the distances between the ideal shape and the non-ideal surface. In reality, there are an infinite number of distances between the two surfaces. Norms are mathematical concepts that transform these distances into a single distance while satisfying certain mathematical properties. The constructed PC-DMIS Primary Datum Plane supports three norms:

- L1 - This is equal to the sum of the distances.

- L2 - This is equal to the square-root of the sum of the squares of the distances. Minimizing the L2 norm is the same as a least-squares fit.

- L∞ - This is equal to the maximum distances between the ideal surface and the non-ideal surface. Minimizing the L∞ norm is the same as minimizing the maximum deviation, so we use the term "minmax" for this norm.

The fitting process minimizes the distances according to the selected norm.

Outside-Material Constraint

Outside-material constraint is also known as a constrained fit. When fitting ideal geometric shapes to non-ideal surfaces, it is possible to add constraints to the fitting process. An outside material constraint means the fitting process is constrained while minimizing the norm. The constraint is that the ideal surface must lie outside the real surface. This is similar to a surface plate. A surface plate is always outside the part. For example, a constrained L∞ plane minimizes the maximum deviation out of all planes that lie external to the part.

Putting It All Together

The PC-DMIS Primary Datum Plane uses the concepts of void filtering, norms, and outside-material constraint together. From the provided measurements of the actual surface, the Primary Datum Plane first filters out the voids. It then finds the plane that minimizes the chosen norm of the distances to the void-filtered surface, subject to an outside material constraint.

#### Examples

The three math types that the Primary Datum Plane exposes have different behaviors in different circumstances. These examples illustrate those circumstances. They also demonstrate how the L2 algorithm gives a repeatable approximation of a physical datum (such as a surface plate).

- L∞ usually gives a result controlled by the edges of the part. This makes it undesirable in most cases.

- L1 behaves somewhat like how a part would rest on a surface plate under the influence of gravity, but it does not handle rocker conditions gracefully. A rocker condition is when a part might rock on a surface plate instead of having obvious stable contact points. A convex datum plane results in a rocker condition.

- L2 performs much like L1 in many cases, but in rocker conditions, it always gives an equalized solution. This is the recommended norm for most applications.

Sinusoidal Surface Profile Examples

In each illustration, the dotted gray line is the real surface feature. The solid black line is the void-filtered surface (the external envelope).

L∞

The red line is the constrained L∞ plane targeting the external envelope (constrained minmax type in PC-DMIS). Observe how this plane is tilted with respect to how a surface plate would work.

L1

The blue line is the constrained L1 plane targeting the external envelope (constrained L1 math type in PC-DMIS).

L2

The green line is the constrained L2 plane targeting the external envelope (constrained L2 math type in PC-DMIS)

V-Like Surface Profile Examples

In each illustration, the solid black line is the void-filtered surface (the external envelope).

L∞

The red line is the L∞ plane targeting the external envelope (constrained minmax type in PC-DMIS). Observe how this plane equalizes the rocking condition.

L1

The blue line is the constrained L1 plane targeting the external envelope (constrained L1 math type in PC-DMIS).

L2

The green line is the constrained L2 plane targeting the external envelope (constrained L2 math type in PC-DMIS). Observe how this plane equalizes the rocking condition.

Wiggly Surface Profile Examples

In each illustration, the dotted gray line is the real surface feature. The solid black line is the void-filtered surface (the external envelope).

L∞

The red line is the L∞ plane targeting the external envelope (constrained minmax type in PC-DMIS). Observe how this plane is tilted with respect to how a surface plate would work.

L1

The blue line is the constrained L1 plane targeting the external envelope (constrained L1 math type in PC-DMIS).

L2

The green line is the constrained L2 plane targeting the external envelope (constrained L2 math type in PC-DMIS).

#### Migration

From earlier PC-DMIS versions to PC-DMIS 2019 R1:

A High Point Plane feature becomes a Primary Datum Plane feature with a constrained L1 math type.

A Tangent Plane becomes a Primary Datum Plane feature and the math type is preserved.

From PC-DMIS 2019 R1 to PC-DMIS 2017 R1 through PC-DMIS 2018 R2:

The Primary Datum Plane feature becomes a Tangent Plane feature.

From PC-DMIS 2019 R1 to PC-DMIS version 2016.0 (or earlier):

If the PC-DMIS version supports the High Point Plane, the Tangent Plane feature becomes a High Point Plane feature.